A novel competition dialysis assay was used to investigate the structural selectivity of a series of substituted 2-(2-naphthyl)quinoline compounds designed to target triplex DNA. The interaction of 14 compounds with 13 different nucleic acid sequences and structures was studied. A striking selectivity for the triplex structure poly dA:[poly dT](2) was found for the majority of compounds studied. Quantitative analysis of the competition dialysis binding data using newly developed metrics revealed that these compounds are among the most selective triplex-binding agents synthesized to date. A quantitative structure-affinity relationship (QSAR) was derived using triplex binding data for all 14 compounds used in these studies. The QSAR revealed that the primary favorable determinant of triplex binding free energy is the solvent accessible surface area. Triplex binding affinity is negatively correlated with compound electron affinity and the number of hydrogen bond donors. The QSAR provides guidelines for the design of improved triplex-binding agents.